Converting a regular bike into an ebike with the BBSHD is so much fun! I just completed this process a couple months ago and have been absolutely loving it - I commute 50 km round trip currently. I have a Kona Fire Mountain trail bike, which is a hard-tail. I'd definitely recommend something with full suspension, as at some point I'll probably get one of those and switch my kit over to that. For now, I can put up with the bumps. You definitely want a solid bike - aka not something from Walmart. I personally can't say what used brands/bikes are good, personally I'd just look at what's on Craigslist and then do some research on the bike/brand to read reviews. You'll probably be looking at trail/mountain bikes - but not the Mongoose/Huffy/whatever Walmart carries. There are lots of solid brands that I've never even heard of. Disc brakes are a no-brainer, you want to be able to stop quick. Another main consideration is having room for the battery in the middle part - if you look at the batteries from LunaCycle, they have great measurements, just make sure the rear shock (assuming it's a full-suspension bike) won't ever hit where the battery will sit. My battery is huge and takes up nearly the whole triangle of my hard-tail, but they have ones that are water bottle shaped.
I'm still learning myself, but I've learned lots and have tons of information for you if you're interested. It sounds like you're where I was a few months ago, just looking into it. Feel free to fire any questions you may have my way, and I'll do my best to help out. Perhaps we could even arrange a meetup sometime if you wanted to check my build out and/or help you assemble your kit as I'm not too far from you (downtown Toronto currently, moving to somewhere in Scarborough in a couple months).
In answer to your questions:
What bike... ha! Tons of options. Whatever is sturdy and a decent price on craigslist (I'd look to spend $400-$800 for something solid that's a decent deal).
The main restriction with a mid-drive is the size of the "bottom bracket", aka the part of the frame that the pedals attach to. Unless you're looking at a fat bike (with huge 4 inch tires or so) you probably won't have to worry about that, it will either be 68 mm or 70 mm and the main kit from Luna Cycle fits both of those. The other issue is that you now have lots of power on the chain, so you may want to upgrade from the stock one to something more sturdy so you don't snap it. I haven't specifically measured my chain for wear yet, but haven't seen any other signs of wear either (the gear teeth start looking different).
Full suspension is definitely more comfortable on your rear end when you hit a pot hole, or anything other than smooth pavement for that matter. Good front suspension is also much nicer on your wrists.
I'd definitely do disc brakes - I have hydraulic (aka fluid in the tubes rather than a cable), personally I think mechanical disc brakes (with a cable) are easier to fuss with but supposedly not quite as nice.
You do not want a Walmart special. Like I said, you're going to have a lot more power that just your legs, which is what all these bikes were designed for. Best case you'd end up breaking something that didn't cause you to crash. Worst case you'd snap an axle or a few spokes and hit the road while going at a pretty good clip - not good! You want a strong bike with strong parts.
